Transmyocardial revascularization (TMR) is an alternative technique to bypass surgery for increasing blood flow to the heart muscle. It involves the puncturing of the heart wall with a laser to form a plurality of holes which heal on the outside but remain open on the inside of the heart, to provide an alternative source of blood to the heart muscle. This technique has been employed on a stilled, by-passed heart using a CO.sub.2 laser with a hand-piece which rests on the heart in order to ensure that the laser beam focus occurs at the correct point on the heart. Recently, a dramatic improvement in TMR has enabled this technique to be used on a beating heart without the need to slow or still it. This has been accomplished with an innovative synchronizing approach disclosed in one or more of the U.S. patent applications listed above under Related Cases and incorporated herein by reference. However, this has introduced new problems. A beating heart is electrically active; the contact of a handpiece against the heart wall disrupts that electrical activity and interferes with the heart function. Arrhythmia and fibrillation can occur and can result in heart failure. Further, any interference with the electrical field of the heart interrupts the synchronous operation of the laser so that the laser is no longer constrained to fire at the optimum moment in the beating heart cycle. The current handpieces used with CO.sub.2 lasers have a relatively sharp tip on a gauge rod extending from the end of the handpiece used to consistently position the handpiece at the proper distance from the stilled heart wall for accurate laser beam focusing and impingement. Such a tip creates increased pressure on the heart, which can cause arrhythmia, fibrillation, and can even puncture the wall of the heart. Further, with these handpieces it is difficult to maintain the laser beam perpendicular with the wall of a beating heart as is necessary to effect clean, correctly placed holes in the heart wall.